Question

A Styrofoam box has a surface area of 0.73 m and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0°C, and the outside temperature is 25°C. If it takes 8.4 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of the Styrofoam W/m-K

Answer 1

`K = 0.076 W/m K`

Step-by-step explanation:

Heat required to melt the complete ice is given as

`Q = mL`

here we have

m = 5.0 kg

`L = 3.35 * 10^5 J/kg`

now we have

`Q = (5 kg)(3.35 * 10^5)`

`Q = 1.67 * 10^6 J`

now the power required to melt ice in 8.4 hours is

`P = (Q)/(t) = (1.67* 10^6)/(8.4 * 3600 s)`

`P = 55.4 Watt`

now by formula of conduction we know

`P = (KA(\Delta T))/(x)`

now we have

`55.4 = (K(0.73 m^2)(25 - 5))/(0.02)`

`K = 0.076 W/m K`